


q.e.d. i love you

by chewhy



Series: haikyuu college shenanigans [1]
Category: Haikyuu!!
Genre: Alternate Universe - College/University, Architecture Major Yamaguchi, Fluff, M/M, Math Major Tsukishima, Math and Science Metaphors, Mathematics, Pining, Tsukishima POV
Language: English
Status: Completed
Published: 2020-09-05
Updated: 2020-09-05
Packaged: 2021-03-06 19:16:24
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 7,205
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/26304022
Author URL: https://archiveofourown.org/users/chewhy/pseuds/chewhy
Summary: “Tsukki? You’ll go with me, right?”He’ll have to socialize, that’s for sure. It’ll be painful. Very painful. Especially if, as Yamaguchi informed him, those other loud, annoying freshman in the double down the hall will be in attendance as well. His ears already ring from the thoughts of “Hinataboke” and “Kageyamaosama” or whatever their damn names are being shouted through the thin walls of their room constantly.But… Yamaguchi will be happy. He might even show some of his designs to Tsukishima if he’s feeling particularly confident and a little bit tipsy.The calculations are pretty obvious, Tsukishima decides with a sigh.“Fine. But don’t expect me to play any stupid drinking games.”The Tsukishima-Yamaguchi Theorem: in which a math major falls in love with the architecture student who lives across the hall and learns to define his feelings through a series of proofs.
Relationships: Hinata Shouyou & Kageyama Tobio, Tsukishima Kei/Yamaguchi Tadashi
Series: haikyuu college shenanigans [1]
Series URL: https://archiveofourown.org/series/1913188
Comments: 34
Kudos: 196
Collections: TsukkiYama Week 2020, chewhy's completed commissions





	q.e.d. i love you

**Author's Note:**

  * For [strawhatmikans](https://archiveofourown.org/users/strawhatmikans/gifts).



> hello thank you for reading my math major!tsukki fic where i projected all of my math major woes onto tsukki hehe also cant believe i missed tsukkiyama week by a hair grr
> 
> commission for my lovely darling serena <3 this is my first commission :D how exciting :D hope u like it! this is also coincidentally my first haikyuu fic so yay! new horizons! 
> 
> note: a full appendix of math terms/references can be found at the end of the fic for reference, but you should be able to read it without that

**_Assume your parameters. Definitions, axioms, theorems._ **

“Hello.”

Tsukishima ignores the timid voice behind him, choosing rather to continue opening suitcases and unpacking his clothes. The weather is hot outside, and the air conditioning is shoddy, blowing just barely enough air to be a tantalizing taste of refreshing coldness across the stream of sweat that runs down his back. He’d rather unpack quickly so he can lie down on the bed or the floor and simply not move. 

“Um, hello?”

Tsukishima turns with a sigh, leveling the timid boy standing in his doorway with a lazy glare. “Mm?” he asks, raising one eyebrow as the only amount of acknowledgment he can spare. 

“Ah!” the boy says, straightening up with alarm. Tsukishima wants to laugh a little bit at that; why is _he_ the one getting startled in this situation? The boy clears his throat, fidgeting from foot to foot as he continues in a soft voice, “Um, my name is Yamaguchi Tadashi! I’m a freshman, or well, I guess that’s kind of obvious since we all are. Ah, I actually live across the hall from you.” He points behind him to gesture vaguely down the hall and Tsukishima turns back to his luggage. 

“Did you need something?” he asks without even bothering to turn around. 

“Right, sorry,” Yamaguchi answers. There’s a soft patter of feet as he steps into Tsukishima’s room and stops just behind him. “I just wanted to ask if you knew how to connect to the internet? Or I can probably go ask the IT help desk if you’re busy, I wouldn’t want to–”

“Here,” Tsukishima says, holding out his hand.

“What?”

Tsukishima turns finally, rolling his eyes as he stares up at the other boy from where he kneels on the ground. “Hand me your phone or computer or whatever.”

There’s a beat of awkward silence as Yamaguchi stares down at Tsukishima’s open hand and Tsukishima stares up at the little tuft of hair that sticks up from the center of Yamaguchi’s head before he shakes his head (and Tsukishima watches the fluff of hair wiggle back and forth). “Right! Here,” Yamaguchi says, passing over his phone. “I got it on my computer, but I had to install an application for that so I didn’t really know how to do that on my phone and–”

Before Yamaguchi’s sentence is even finished, Tsukishima is holding his phone back out to him. “You talk too much. Have you unpacked already?”

Yamaguchi blushes bright red at that, bobbing his head as he answers, “Um, yes. I had an early move-in slot.”

Tsukishima hums thoughtfully before turning to point at a yet unopened box. “Help me set up my shelves, then.”

“Me?” Yamaguchi asks in surprise. 

Tsukishima snorts, “Do you see anybody behind you? Anyway, I helped you with your internet. Your turn to help me now.”

It’s somewhat logical, Yamaguchi acknowledges, so he squats down to stab at the cardboard with his keys while Tsukishima continues to put away his clothes. 

And that’s that. 

–

**_Proof by contraposition: prove “if p then q” by showing “if not q then not p”._ **

Wherever Tsukishima goes, Yamaguchi follows. Wherever Yamaguchi goes, Tsukishima is bound to make an appearance. 

Tsukishima isn’t entirely sure how it happened. They’d gone together to orientation and floor events, finding some solace in knowing at least one person by name in rooms full of thousands of other freshmen. Then they’d come to some unspoken agreement to find each other in the carrels of the library’s third floor between classes on the west campus, even though Tsukishima was always coming from the engineering quad two full blocks away, dragging himself away from dusty chalkboards and piles of yellowed textbooks in the small corner of basement designated to the math department. 

He’d tap his foot waiting, impatiently rifling through the books of the Arabic literature section that he couldn’t even read until Yamaguchi stumbled over with an armful of sketchbooks from the design and architecture building just down the street. 

“Tsukki!” Yamaguchi would call loudly, waving a hand with a bright smile only to duck down in embarrassment when some third year would inevitably hiss at “the damn freshman” to “just shut the fuck up already, don’t those idiots know this is the silent floor”. 

Now, though… Now it’s spiralled completely out of hand as Yamaguchi looks up at him through big puppy eyes as he’s all “but Tsukki” this and “aw, Tsukki” that, tugging on the back of his shirt as he tries to work through a problem set that’s not due for another whole week. 

“Yamaguchi,” Tsukishima says, halting him in his tracks. Tsukishima’s voice is by no means thunderous or booming. In fact, he’s been told before that it’s rather reedlike and _irritating_ if anything else, especially paired with that delightfully fitting sneer he usually carries on his face. When he turns around, though, Yamaguchi looks absolutely devastated, completely and thoroughly chastised as he bends his neck to keep his eyes on the floor, and Tsukishima sighs. “Yamaguchi,” he says again, this time letting the last syllable drag on just a hair longer. That bare millisecond, some insignificant _epsilon_ amount of time, is somehow enough. Yamaguchi’s face looks up at him now with a tiny ray of hope. 

“Tsukki? You’ll go with me, right?”

Tsukishima weighs his options. Skip the party and there are two distinct outcomes. Yamaguchi will either end up sad on his floor pretending not to drown in his FOMO as he flips through Tsukishima’s dry math books. Or he’ll be a drunk mess, all by himself with nobody to watch out for him getting drugged or murdered or poisoned, probably making a whole fool out of himself while Tsukishima sits back safe and sound in his dorm room, not knowing what could possibly be happening to Yamaguchi unattended. 

Then on the other hand, if he goes to the party… 

He’ll have to socialize, that’s for sure. It’ll be painful. Very painful. Especially if, as Yamaguchi informed him, those other loud, annoying freshmen in the double down the hall will be in attendance as well. His ears already ring from the thoughts of “Hinataboke” and “Kageyamaosama” or whatever their damn names are being shouted through the thin walls of their room constantly. 

But… Yamaguchi will be happy. He might even show some of his designs to Tsukishima if he’s feeling particularly confident and a little bit tipsy. 

The calculations are pretty obvious, Tsukishima decides with a sigh. 

“Fine. But don’t expect me to play any stupid drinking games.”

–

**_Proof by mathematical induction: if P(n) is true, and P(n) being true implies that P(n + 1) is true, then P(n) is true for all natural numbers n._ **

“I don’t get it.”

Tsukishima sighs and presses his fingers into his temple. “What is there _not_ to get, all you have to do is go in a circle and count. Can you even add to one?”

“Uh. Seven,” Hinata says, somehow managing to slur three simple syllables together. 

_No stupid drinking games my ass_ , Tsukishima thinks with a growl as he leans back into the sticky couch. He’s not sure if it’s a result of the humidity, sweat, or drinks that have spilled all over it, but he decides it’s disgusting anyway. Out of the corner of his eye, he watches as Yamaguchi sips on a beer, making an obviously disgusted face at the taste even as he chokes it down at the encouragement of some of the upperclassmen (Fishy something? Tank?) egging him on. 

The one saving grace of the night is that it’s not some hyped up frat rager that Yamaguchi’s dragged him to. He’d apparently met some nicer second years in the club he’d joined earlier in the semester while Tsukishima had been busy begging around for an assistant position in the math department. To Yamaguchi, this means that all of his new friends are also all Tsukishima’s new friends. 

To Tsukishima though…

“Okay. And what’s seven plus one?” 

“Oh, I know this one! Eight.” Kageyama’s the one answering this time and he’s in no better state. His face is flushed red all the way down his collarbones and he leans heavily against a lamp in an attempt to stall his swaying. “Idiot,” he sneers down at Hinata, who’s sprawled on the floor after what could barely have been a half shot of vodka. “I can count _so_ much higher than you.”

Tsukishima _really_ wants to bash his face into a wall right now. “How did you guys even get into the same university as me?” It’s really not meant to sound so condescending. (Okay, maybe a little bit.) He’s just genuinely curious. 

With eerie synchronization, they both turn to him together and answer with a shrug, “Sports scholarship.” That sets them off in another fight as they hiss and claw at each other and Tsukishima stands with a final sigh. 

So much for teaching them Cheers to the Governor. 

“Tsukki!” Yamaguchi says, giggling as Tsukishima comes up behind him. “Have you guys met Tsukki yet? This is Tsukki!” 

Clearly, he’s not in a much better state than either of the idiot duo still rolling on the floor a few feet away, but he manages to make it so much more endearing than them. “Drink some water, Yamaguchi,” Tsukishima says instead, holding a hand over Yamaguchi’s beer. 

“Oh, so _you’re_ the grand Tsukki, huh?” the bald one says, leaning aggressively into Tsukishima’s face. 

“It’s Tsukishima,” he answers blandly, looking down his nose at the other guy. 

“Tsukki! We’ve heard so much about you, haven’t we, Tanaka?” the shorter one says, running his eyes up and down Tsukishima’s form in a distinctly terrifying way. 

Subconsciously, Tsukishima finds himself taking a step away from the shorty which results in him stepping back onto Yamaguchi’s toes. 

“Ow!” Yamaguchi whines with a yelp from behind Tsukishima and in his hurry to step off and out of the way, Tsukishima’s gangly limbs somehow get caught on something somewhere and he ends up in a heap on the floor with Yamaguchi gathered in his arms, lukewarm beer seeping into the sleeve of his hoodie. 

The two upperclassmen snicker from beside them, whistling as they go off to grab some paper towels and Tsukishima growls after them. 

“I’m sorry, Tsukki,” Yamaguchi’s voice calls out, bringing Tsukishima back to his present predicament. Tsukishima’s about to snap back some retort about how it’s not even Yamaguchi’s fault anyway when he interrupts him. “You’re not having very much fun here, are you?”

Tsukishima doesn’t respond. He’s never been one for empty words and pretty reassurances, especially if they’re all just lies anyway. His expression probably makes it clear enough regardless. 

Yamaguchi sighs, sounding more sober than he had moments ago as he wipes at Tsukishima’s hoodie with his own sleeves, dabbing the wetness around. “I just thought, since Sugawara is so cool, and all of the people _he’s_ friends with are so cool, well, you’d get along with them. And we could all be friends and stuff, you know?”

Tsukishima wrinkles his brow. He doesn’t quite follow this drunken, rambling attempt at logic. 

Yamaguchi must pick up on that because he laughs and scratches the back of his head, leaning back against the counter so their legs are tangled together on the sticky floor. “You know. Cuz I think you’re cool, too. Transitive property or something like that, right?”

Tsukishima blinks, lips falling open a mere half centimeter. To him, though, that’s a sign that he’s been blown away in surprise. Looking back on this moment later, Tsukishima will probably blush when he remembers how Yamaguchi called him “cool” too, but at this particular second on this plane of existence on the spacetime continuum or whatever Einstein wen on about, his mind won’t stop revolving around one fact. 

“That’s not even how the transitivity relation works, dumbass.” 

Yamaguchi, architectural design student at Karasuno University, has been listening to Tsukishima’s long-winded explanation of proofs and formulas. Enough to, at some point, pick up on what the transitive property is. 

Yamaguchi pouts at him and the moment is broken as the shorty comes jumping down on them with an armful of paper towels while baldy lobs globs of damp tissue at them from across the room. 

They’re annoying as hell, but if Yamaguchi likes them, then well…

Tsukishima supposes he’ll just have to learn how to tolerate them, too. 

– 

**_Proof by construction: construction of a concrete example with a property to show that something having that property exists._ **

“No.”

“Aw, come on! Kageyama, you tell Tsukishima that he has to come to movie night!” Hinata is absolutely _vibrating_ where he stands and Tsukishima can’t bear the sight of him twitching in the corner of his vision. 

“Tsukishima. Come.”

“What, you think I’m some dog? Some mongrel that should listen to royalty like you, huh?” Tsukishima goads, tilting his head back just far enough to make his sneer visible to Kageyama across the room. His target is missed, however, as Kageyama seems far too focused on poking at the cactus Tsukishima has sitting on his windowsill. 

“Kageyama!” Hinata pouts and only receives a half-hearted shrug in return. 

“I tried.”

“You did not! You did not even make an _attempt!_ ”

“Yes, I did! Don’t tell me what I did or didn’t do!”

Tsukishima tries his best to zone the two’s bickering out of his mind as he goes back to read the page he’s been stuck on for the tenth time when his door opens with a click to reveal Tadashi smiling at the chaos of Tsukishima’s dorm room. When Tadashi’s eyes trail past Hinata and Kageyama’s strange mating dance, Tsukishima finds himself ripping his own gaze back down to his book. 

There’s nothing to be guilty about, it’s just that, well…

“Tsukki,” Tadashi says, stepping over to lean against his bed frame. Even with the idiot duo’s yelling in the background, Tadashi’s voice, however soft, will always be heard. “You’re coming to movie night with us, right?”

Tsukishima grunts, lifting one hand slowly to settle his glasses back at the top of his nose bridge as he stalls for an answer. 

“Please?”

How can he ever say no to a face like that? 

“Fine.”

The room is suddenly silent as both Hinata and Kageyama turn slowly together to face him. 

“Hey, how come you said no to us but when _Tada_ –”

“Out,” Tsukishima says, pointing one arm to his door as he growls in a voice that leaves no room for argument. As stupid as the two of them may be, it seems they have a shred of survival instincts still remaining somewhere in their walnut-sized brains as they trip over each other in their haste to make it out of the room. 

Tsukishima sighs as he flops back on his bed, staring up at his ceiling as he resents the fact that his room is considered the “big room” of their hall. 

“Do you want me to leave, too?” Tadashi’s voice asks, drifting slowly down to Tsukishima’s ears. 

Tsukishima holds out a hand, groping around blindly at the air until he comes into contact with Tadashi’s wrist so he can pull him down onto the bed next to him. 

“No, Tadashi. Stay.”

He can’t quite remember when Yamaguchi became Tadashi. It doesn’t really matter though. 

–

He regrets it. You could try asking what exactly it is that Tsukishima regrets, but he wouldn’t be able to come up with a coherent answer to that, other than _all of it_. He mostly regrets not ever being able to say no to Tadashi’s stupid, idiotic, beautiful, adorable puppy dog eyes. 

Currently, however, Tsukishima mostly regrets sitting down on the couch first while everybody else bustled about preparing snacks and drinks, searching for old DVDs between cracks in the couch cushions, or even going to the bathroom before the movie started. 

On one side of him, he has Asahi who’s currently using Tsukishima’s shoulder as a large, warm tissue and on the other side of him, he has Tanaka, who’s clenched Tsukishima’s bicep so hard it’s surely going to leave bruises the next day. It also doesn’t help that Tanaka has apparently watched this sappy romance drama enough times to be able to recite the whole thing from memory, word for word under his breath (and coincidentally, directly into Tsukishima’s ear). 

When the movie ends and somebody flicks the lights on, Tsukishima thinks he’ll finally be freed as he sends (the mildest, most non-pathetic) pleading looks towards Tadashi, but Tadashi only laughs at his agony. 

“That was so heartbreaking,” Asahi sobs into Tsukishima’s chest. Tsukishima isn’t entirely sure how to comfort anybody on a normal day, so when a six and a half foot tall, goatee and ponytail wearing man is losing it all over his lap, Tsukishima’s even more at a loss. Especially when taking into consideration they’d just watched a romantic _comedy_. 

“There, there,” Tsukishima mutters, trying his best to keep the sarcasm in his tone at a mild seventy percent. It seems to catch Daichi’s attention, though, from where he sits on the other side of Asahi as he rubs at his chin thoughtfully. 

“You know,” he says and Tsukishima’s already dreading whatever is going to come out of his mouth next. “You kind of remind me of the main love interest, Tsukishima.”

“Excuse me?” His hand stills on Asahi’s back where it’s been trying to push him off, lightly disguised as aggressive patting. Tadashi looks up at Tsukishima in interest then, tilting his head to the side as if to imagine it. 

“Yeah, I kind of see it! And not just because he wears glasses. You both _are_ kind of the cold and snarky type,” Tadashi says, eyes sparkling as he laughs at Tsukishima’s indignation. 

“You’re _exactly_ the tsundere type, Tsukishima,” Daichi says. It’s really more of an announcement than a comment and beside him, Tanaka is starting to look at him with dangerously starry eyes. “You pretend to be mean and cold, but you really care about everyone a lot, don’t you?”

“No. I hate all of you,” Tsukishima answers levelly, glaring down at the giant, hairy man-baby still whimpering against his thighs. “I truly despise you all.”

“Not me, though! Right, Tsukki?” 

Tsukishima’s glare softens at that, no matter how much he wills it not to. “Whatever.”

“And see, that’s something else funny!” Daichi says, pointing one finger from Tsukishima to Tadashi, from Tadashi to Tsukishima. “Yamaguchi, you remind me of the main character, too! So kind and timid.”

At that, Tadashi freezes up, shaking his head as his mouth shapes silent words of rebuttal. 

“Ohhh!” Nishinoya screams, jumping onto the back of the couch behind them. Tsukishima’s heart drops in his chest, but he stares cooly down his glasses at the shorty anyway. “Then that makes… Tsukishima and Yamaguchi lovers!”

“Ahhh!” Tanaka wails (right into Tsukishima’s ear). “How is it that all of the mean guys end up with the cute and nice character? Should I start acting mean and distant, too?”

Tsukishima refuses to miss such a perfect opportunity for a jab, smirking as he scrubs Tanaka’s fuzzy head with one hand. “With a face like yours, people would just think you’re a thug, you know? Best to leave that kind of persona for the professionals.” 

Even as he eggs Nishinoya and Tanaka on, Tsukishima doesn’t take his eyes off of Tadashi and the thoughtful blush that overtakes his face. 

–

**_Proof by contradiction: if some statement is assumed true, a logical contradiction occurs, hence the statement must be false._ **

It’s been weeks since that ridiculous movie night and Tsukishima has long since dumped his hoodie in a vat of bleach after multiple failed attempts to get Asahi’s snot stains out of the sleeves. Outside of those disgusting souvenirs, another part of that night has been itching at the back of Tsukishima’s mind for days. 

He’ll be standing in front of a chalkboard, ready to let his mind flow and let the puzzle pieces of his proof fall perfectly into place, only to discover by the end that half of the board just has the words “Yamaguchi Tadashi” scribbled all over it. He grits his teeth in embarrassment and goes to erase the board quickly, looking behind him to see if anybody’s willingly made their way down into the dust-covered math library and caught him in this moment of foolishness. 

Tsukishima sighs, discarding his chalk to the side and sits back in a chair, knowing his concentration’s been absolutely shot. 

“Yamaguchi Tadashi,” he says out loud. It feels unnatural to say his last name now. As if they’ve been friends since childhood, calling their given names out to each other for eighty percent of their lives, and not just for a small fraction of the last few months that they’ve known each other. 

He looks down at his chalk dusted fingertips and wonders for just the shortest second what it would be like to hold–

“No!” He lightly smacks himself in the face for good measure, only to end up with a handful of chalk dust flying into his mouth. “It was just a stupid joke. I do _not_ have feelings for Tadashi. We are friends, nothing more.”

It doesn’t seem to be working. Tsukishima will kill whoever the hell came up with the concept of manifestation because it’s absolute and utter bullshit. 

A light ruffle of air-conditioned wind pushes one of his scrap pages down to the floor, and Tsukishima looks at it for a moment before leaning down to pick it up. 

“Hmm,” he hums, looking down at it. “I don’t have feelings for Tadashi. I just need to… I need some space. I need to focus on school, anyway. And we don’t need to hang out all the time or anything. In fact, it’s probably not necessary at all. We’ve just been spending too much time together.”

Tsukishima isn’t sure who he’s trying to convince at this point. 

–

“Tsukki!”

Tsukishima walks on, taking the stairs two at a time and shoving his chin further down into his collar so he can avoid seeing Tadashi’s disappointed face. 

–

“Hey, Tsukki! Did you–”

He barrels forward, frown twisting further down on his mouth.

–

“Hey, four-eyes.”

Tsukishima glances back at Kageyama, raising one eyebrow in response. 

“Tadashi was looking for you,” he spits out through gritted teeth. 

Tsukishima is sorely tempted to take a jab at Kageyama, call him a royal pain in the ass or whatever but Tadashi’s name falling out of this bastard’s mouth has him twitching away instead. 

“Tell him I’m busy.”

He walks away, quickly. Before Kageyama can call after him. Before Tadashi can catch up to him. 

–

“Tsukki?”

 _Fuck_. Muscle memory had brought him to their carrel (although he doesn’t even remember when one of the carrels became _theirs_ ), but he hadn’t expected to see Tadashi waiting there still after a whole week of skipping. 

Tsukishima doesn’t answer, just turns away and listens to the squeak of his sneakers echo on the tile flooring. A senior attempts to hush him from among the bookshelves, but one look at Tsukishima’s face has her walking far in the other direction. 

–

It’s hell. It really is. Tsukishima lies back on his bed, throwing a stress ball up and down above his face. Its bright, yellow smiley face taunts him, and Tsukishima sighs, turning over onto his side as he contemplates what to do, alone with all this free time he never noticed he had. 

He’d study but unfortunately, he’s all caught up and reviewed two weeks ahead into the syllabus. Anything else that he can think to do, he’s afraid of running into Tadashi because at some point in his short college career, Tsukishima’s life had begun revolving entirely around Tadashi this and Tadashi that, a centripetal force of motion he can't escape. 

A small crinkling noise catches his attention and he looks up just in time to see a small square of paper being slid under the door. 

With a frown and a sigh, Tsukishima musters up some energy to walk over and pick up the page. 

The letter starts off, as expected, like this: 

_Tsukki!!!!!!!!!_

As he reads on, his eyebrows grow only more and more furrowed and he clenches the note between his two fists. 

_I’m sorry, Tsukki. Whatever it is you’re mad about, I can fix it! I’ll do better, so just talk to me, okay? I really miss you. You’re my best friend here, you know? Watching Hinata and Kageyama fight over squirrels just isn’t fun without you around, I guess. Anyway, just let me know if there’s anything I can do. I know you’re probably really busy with all of your fancy math stuff. You’ve always been smart, though, so I know you don’t have to be studying so hard!_

It goes on and on in typical rambling Tadashi fashion, and the frown on Tsukishima’s mouth quirks up a little as he continues to read the words written in dark green ink on Tadashi’s special stationery that he bought for sending letters to his family. 

Tsukishima sighs, crumpling up the letter and letting it fall back down to the floor. He’s had enough fucking space. It’s time to confront the issue, because something _somewhere_ went wrong, and it sure as hell wasn’t Tadashi’s fault. 

– 

**_Proof by exhaustion - divide it into a finite number of cases and show it is true in every case._ **

It hits him like a lightning bolt, a strike of inspiration the same way Issac Newton must have felt when that apple fell on his head with the full weight of gravity and the future of physics. 

Tsukishima is… Well, he’s…

He’s in love. With Tadashi. 

The apple he’s holding falls out of his hand and rolls across the cafeteria floor, bouncing lightly off of somebody’s foot. 

At least he _thinks_ he’s in love with Tadashi. It’s hard to tell when he’s never even liked anyone, much less loved anybody before. 

A hand reaches down to pick up the apple and Tsukishima watches a familiar pair of sneakers walk towards him until his view is obscured by the apple being held up to his face. 

“Tsukki?”

“Tadashi, I…”

Tadashi smiles, warm and bright and welcoming. Always so eager to forgive and accept all of the disgusting and pathetic parts of him, even after he’s done absolute jack shit in return. 

“Tsukki! Your face looks so tired, have you been doing alright?” Tadashi jumps back in as if nothing has changed between them. 

Maybe this is–

Tadashi grabs his hand and Tsukishima startles. Tadashi takes Tsukishima’s fingers, one by one, and wraps them around the apple he’d dropped just moments ago. “Tsukki, I missed you.”

Yes. This is love. 

The nodes of freckles on Tadashi’s cheeks, the way Tadashi’s hands are always warmer than his, the slouch in Tadashi’s posture as he fits right up against Tsukishima’s side. All of these things. The extra bowl of ice cream that Tadashi holds out with Tsukishima’s favorite flavor, the backpack Tadashi moves down from a seat that’s clearly been saved, the eagerness to fill Tsukishima in on all that he’s missed these past couple of barren weeks. 

All of these things. 

– 

It’s the way Tadashi will tug on Tsukishima’s sleeve to ask him to double-check the math on the angles in his sketchbook, even though Tadashi is much better at simple arithmetic. 

“You’re a math major, aren’t you?” he teases and Tsukishima rolls his eyes and grumbles something about how that level of math can be done with a calculator when what he really means is “I love you”. He looks over the math anyway, if only as an excuse to get a peek at the designs Tadashi draws out. 

– 

It’s the way leaves are scattered throughout Tadashi’s hair as he rolls on the ground, shouting out, “Catch one, Tsukki! It’s good luck!” as he swipes at the orange, yellow and brown that falls through the air. 

“I think you’ve caught plenty with that shag of yours anyway,” Tsukishima answers with a wry grin. He holds out a hand anyway and watches as a single yellow leaf floats down into his palm. It’s brittle and dry. He could crush it between his fingers so easily. 

Instead, he unzips Tadashi’s backpack (because of course he’s holding Tadashi’s backpack while Tadashi runs out to frolic with the other idiot duo in the raked up piles of leaves) and tucks it neatly in between the pages of his sketchbook. 

“Good luck, idiot.”

– 

It’s the way Tadashi falls asleep on Tsukishima’s bed while studying, a highlighter pressed into his cheek and leaving a stripe of bright green that horrendously clashes with his freckles and hair. 

Tsukishima can’t bear to wake him and just tuts at him under his breath, feeling like a mom as he drags a blanket over Tadashi’s shoulder. 

He freezes in his tracks when Tadashi mumbles, just barely audibly, “Tsukki,” before he rolls over and falls asleep. In his constant shifting, Tadashi’s sketchbook is pushed off of Tsukishima’s bed and he winces as it hits the floor with a loud thud, but Tadashi doesn’t react, too busy snoring away. 

Tsukishima bends over with a sigh as the joints in his knees crack loudly, picking up the sketchbook only to freeze once more when he sees it lies open to a page Tadashi has never revealed. 

That’s… That’s himself, staring right back at him. His glasses are slightly askew as if somebody’s smacked him in the face and his face is twisted in an uncommon open-mouthed smile, but that’s definitely him. 

Tsukishima isn’t sure how long he spends sitting there, staring down at the drawing before he’s suddenly blinking himself awake, back aching from the cold, hard floor. His bed is empty and the sketchbook is gone but he can’t seem to wipe the smile off his face, no matter how hard he tries. 

– 

It’s everything that Tsukishima can count, and then also all of the gaps in between that he can’t. 

Every action, every gesture. They all mean one thing. 

“I’m in love with you, Tadashi.”

So why can’t he say it?

– 

**_Combinatorial proof: establish the equivalence of different expressions by showing that they count the same object in different ways._ **

Tsukishima stares down at the pages of notes sitting in front of him. His chin rests in one hand as he scribbles _n_ ’s and _k_ ’s, lines and nodes. Pigeonhole principles and Bolzano-Weierstrass theorems morph under his hand as he yawns, drawing little lines and equations to calculate how many lunches he’s bought Tadashi in one semester. He flips the page idly, reviewing the counting trees on his page as he hides a yawn behind his hand. 

“That wouldn’t work,” Tsukishima muses out loud. “As if anybody could try to measure the way Tadashi makes me feel.”

“What are you muttering to yourself about now, Tsukki?” Yamaguchi stands above him, leaning close into his space and Tsukishima almost falls out of his chair in surprise. 

Of course, he’s far too level-headed to act in such an unbecoming way so he hides his shiver as a shudder of disgust. “Nothing that your little head could possibly wrap around.”

He wonders, though, if Tadashi’s set of love could form a bijection with his own. 

– 

**_Probabilistic proof: an example is shown to exist, with certainty, by using methods of probability theory._ **

Tsukishima realizes that he has two options right now. One, he could continue as normal and live his best life with Tsukishima as his only friend at this university. Two, he could _do_ something about it. He’d lose his only friend. But it’s an impossibly big school, so how hard could it be to avoid him and make some new friends? Everybody kind of sucks, though. Everybody except for Tadashi, and Tadashi’s are not exactly easy to come across. 

What’s the best option that would cut his losses?

“Tsukki, what’s got you thinking so hard?” Tadashi reaches one hand forward, tongue poking out between his lips as he presses one finger to the space between Tsukishima’s eyebrows. “Your pretty face will get all wrinkly if you keep doing that.”

He weighs the probability of rejection against the potential of losing Tadashi someday without even trying and realizes they both hurt.

– 

**_Direct proof: combine definitions, axioms, theorems to arrive at a logical conclusion._ **

Tsukishima lets out a slow breath, pressing his glasses up to the highest peak of his nose bridge. Extreme maxima, hooking where the slope is zero, yada yada math reference. He needs full concentration for this so he can–

“Heyyyy, Tsukishima! What’s with that expression like somebody smeared shit under your nose?”

Tsukishima is _literally_ going to kill Hinata. Unless Kageyama does first. “Shut up, twerp.”

“Hinata’s right, you know. Your face is really ugly right now.”

His eyebrow twitches. Okay, revision. He’s going to kill _both_ of them. Simultaneously. 

Schooling his features into a more neutral position, he turns to smile widely down at them. “Oh? The _king_ is agreeing with Hinata? That’s a first?”

“What?” Kageyama is already bristling, hands clenched into fists as he whirls on Hinata. “No! I am not agreeing with anything that comes out of your stupid mouth!”

“Hey! I didn’t even say anything, why are you yelling at me?”

Using their bickering as a distraction, Tsukishima quickly moves to the next next table over for some peace and quiet, watching as the librarian angrily marches over to drag Hinata and Kageyama away by their collars. If they keep this up, they’ll probably be banned entirely from the library by the second month of sophomore year, but Tsukishima doesn’t have time to worry about that. 

He frowns down at his trembling hands, flexing his fingers as he types and retypes a message. It shouldn’t be this difficult, and it’s really pathetic how many times he has to proofread one sentence for typos but finally, it’s sent and he sits back in his chair, an uncomfortable roll of nervousness coiling in his stomach. 

–

“Tsukki! I got your message, what did you want to ask me?” Tadashi jogs over to him with a little wave and Tsukishima’s not sure what to do about the way his heartbeat spikes in response to seeing Tadashi’s smile. 

“Tadashi.” His voice fails him and he just searches Tadashi’s eyes for answers to a question he’s too much of a coward to ask. Tadashi waits, though. He’s silent and patient, nodding in encouragement as Tsukishima clears his throat with a small cough. 

“Tadashi,” he begins again and realizes only on the last syllable that for once in his life, he has no idea what he’s doing. “Tadashi.”

“Yes,” Tadashi answers, with a giggle, “That’s my name.” He doesn’t say anything else and his eyes are so bright with anticipation, Tsukishima knows there’s no backing out of this one anymore. 

With a final and fourth, “Tadashi,” Tsukishima finds his voice again. 

“We’re friends, right?” What the fuck? That wasn’t what he’d meant to say. 

Tadashi laughs and nods, “I hope so. It would be kind of embarrassing if only _I_ thought we were friends this whole time.”

“Right,” Tsukishima says, sorely tempted to smack himself in the face the way he’s seen Hinata do to wake himself up while reading. “Well, we’re friends. And we’ve been pretty close since we met each other that first day. You’re actually probably my only friend, too. That actually makes you my best friend, which is pretty significant, considering the number of people on campus.” He’s never said this many words in his life before and Tsukishima sorely wishes he could tape his mouth shut the way he’s seen Sugawara do to shorty and baldy during finals weeks. He shakes his head with a scoff at himself and continues, “This is pretty lame, but we eat together a lot. And we meet each other to walk to classes, even if they’re on the other side of campus. We also–”

“Tsukki,” Tadashi interrupts with an exasperated look. “Are you just going to list our daily routine?”

“No,” Tsukishima answers. He totally was, but Tadashi doesn’t have to know that. “I was just going to say that I know your favorite color. It’s yellow. You like to play volleyball for fun. And your favorite constellation is Ursa Major. Coincidentally, one of my favorite animals are bears–” 

Tsukishima’s words stutter to a halt as Tadashi holds out a hand in front of his face. For maybe the first time in Tsukishima’s life, Tadashi looks irritated with _him_. 

– 

**_Proof by intimidation: attempts to advance an argument by marking it as obvious or trivial; often used when the author is an authority in their field._ **

“Honestly, Tsukki, I really don’t know what all you’re going on about. I love you! And it’s obvious that you love me! So why won’t you just let me _do_ something about it!”

Tsukishima finds himself stumbling forward as Tadashi grabs a fistful of his shirt and tugs him forward. Their teeth clash and where Tadashi’s eyes are scrunched tightly shut, Tsukishima’s eyes are blown wide open, going cross-eyed as he tries to count the tessellated fragment of freckles dotting Tadashi’s cheeks. 

_Maybe_ , Tsukishima thinks as he lets his eyes slide shut, _this proof can be left as an exercise to the reader._

* * *

**Author Chewy’s shitty appendix, aka math glossary and proofs related memes explained in layman’s terms:**

I tried to put a simple definition of how each of the listed proof methods works, so I won’t be defining those here unless I want to elaborate on a specific part of it, but feel free to let me know if anything is confusing that I can clarify for you!

 **Axioms** \- basically the basis of math lol like being able to add two numbers is an axiom. It’s the simplest rules of math that can’t be proven - basically, its an axiom if, without this rule, you couldn’t prove the rest of math. The rest of math is made up of theorems that were proved using axioms, and then other theorems that were proved using those already proved axioms plus theorems. I wonder what tsukki’s axioms of love are? Probably: if you like them a tiny bit and they are your only friend, that is love. Everyone else just gets mild apathy at best. 

**Bijection** \- means if you have two sets of things, you can draw one line from a thing in set A to a thing in set B with no shared lines AND no left over things in either set. Basically a one to one connection between each item of either set. 

**Pigeonhole principle** \- this is a fun one that i’m not very good at explaining! Say you have a bunch of pigeons, and every night they fly back to their home and go to sleep in their holes. However, there are more pigeons than there are holes to sleep in. Eg. 51 pigeons and 50 holes. This proves that there is _at least one_ (if not more than one) hole that has two (or more!) pigeons in it. Could be 49 holes with one pigeon and one hole with two pigeons, or it could be 49 holes with no pigeons and one hole with 51 pigeons. Either way, at some point or another one of those holes with have 2+ pigeons in it. That’s the basis of the proof, and u don’t really need to know what it’s used for (unless u wanna know, in which case google it to learn more maths yay!)

 **Contrapositive/contraposition** \- if A then B can also be proved by showing if not B then not A. how, do you ask? It’s like saying “kageyama will stop bickering with hinata when pigs fly” and really what this means is “since pigs will never fly, kageyama will never stop bickering with hinata”. Cool how that works, huh?

 **“The proof is left as an exercise to the reader”** \- universal dick move. Anything along the lines of “the proof is obvious” “clearly, the proof is…” “the proof is trivial” etc. etc. basically when a mathematician is like “hah just trust me bro, i dont even need to prove this bc this should be obvious to you!” but then dumb bitches like me are like “... wait but its not obvious pls explain i dont get it :((((“

 **Induction** \- if you can show that one thing works, and then the thing plus one also works, and then you can ALSO show that the base case works, then that means the base case works and the base case plus one works and the base case plus one plus one works and the base case plus one plus one plus one works… and all the way up to infinity! And all you had to do to get to infinity was show three things! Math is cool, kids!

 **Combinatorics** \- combinatorics is literally just counting but fancy and times a thousand bc u count like big big big time

 **Exhaustion** \- fun note on proof of exhaustion, the current most well known proof of exhaustion is the four colors theorem, which basically says that if u have any map (or basically any criss crossing lines on a page) then u only need four colors to make sure that every shape/state/country on that page will not be touching the border of another country that has the same color as it. Fun fact abt this proof, tho, is that it was the first proof like it that was done by a computer, meaning that some people don’t trust it bc a human hasn’t been able to check that the computer was right! But tsukki doesn’t need a computer to prove that he loves yamaguchi, eh?

 **Lines and Nodes** \- this is just like very straightforward but I like to think of Tsukishima tracing the nodes on Yamaguchi’s face (nodes being like points - google some images if u want a clearer picture!)

 **Tessellation** \- same thing as above, just like to think of Tsukishima seeing shapes in Yamaguchi’s freckles but its basically an infinitely repeating shape that touches edges perfectly w the shape next to it (which is the same shape as itself… also google for images for a better picture!)

 **Bolzano-Weierstrass Theorem** \- bro idek this one tbh like i use it in my proofs for my exams but i dont even understand how it works at the end of the day. Google it for more info i guess, and let me know if you understand how to use it lmfao

 **Epsilon (limits)** \- epsilon is basically a really really really tiny value, and it’s used to calculate the limit of something (think Mean Girls “the limit does not exist!” type question but more complicated cuz honestly Cady is not that smart), so you can prove that an equation/set/limit approaches a number _x_ by showing that the limit is somewhere between _x_ and _x + e_ (e here being epsilon, i dont have a greek keyboard). Since _e_ is so so so tiny, there’s basically no difference between _x_ and _x + e_ at this point, so the limit is equal to _x_. 

**Author's Note:**

> this is my magnum opus. 
> 
> find me on [[twitter (ch3w2)](https://twitter.com/ch3w2)] and [[tumblr (ch3w2)](http://ch3w2.tumblr.com/)]!  
>  **kudos and comments always appreciated**
> 
> my carrd is [b4k95.carrd.co](https://ch3w2.carrd.co/) for more information about requests


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